The equation of motion for an oscillator in vertical SHM is given by y=(0.60m)sin[(130rad/s)t].
Part A
What is the amplitude of this motion?
Part B
What is the frequency of this motion?
Part C
What is the period of this motion?
A. 0.60
B. 20.69
C. 0.048
I Don’t know
Part A:
The amplitude of a motion is the maximum displacement from equilibrium. In this case, the amplitude is given as 0.60 m.
Part B:
The frequency of a motion is the number of complete oscillations per unit of time. In this case, the coefficient in front of 't' gives the angular frequency, which is 130 rad/s. The frequency can be calculated using the formula f = ω/2π, where ω is the angular frequency. Plugging in the value, we get:
f = 130 rad/s / (2π) = 20.68 Hz.
Part C:
The period of a motion is the time taken for one complete oscillation. It can be calculated using the formula T = 1/f, where f is the frequency. Plugging in the value, we get:
T = 1 / 20.68 Hz = 0.0483 s (rounded to four decimal places).
So, the amplitude of this motion is 0.60 m, the frequency is 20.68 Hz, and the period is 0.0483 s.
To find the amplitude of the motion (Part A), you need to look at the equation y = (0.60 m)sin[(130 rad/s)t]. The amplitude of motion is the value that is multiplying the sine function, which in this case is 0.60 m. Therefore, the amplitude of this motion is 0.60 m.
To find the frequency of the motion (Part B), you need to look at the equation y = (0.60 m)sin[(130 rad/s)t]. The frequency is determined by the coefficient in front of the variable t inside the sine function, which is 130 rad/s. The frequency is given by the formula f = ω / (2π), where f is the frequency in Hz and ω is the angular frequency in rad/s. So, in this case, the frequency is f = 130 rad/s / (2π) ≈ 20.7 Hz.
To find the period of the motion (Part C), you can use the formula T = 1 / f, where T is the period in seconds and f is the frequency in Hz. Plugging in the frequency found in Part B, the period is T = 1 / 20.7 Hz ≈ 0.048 s. Therefore, the period of this motion is approximately 0.048 seconds.